This is an Assassin equipment guide (with some skill pointers) for Ultimate Vault Hunter Mode. It's not the only right solution, nor do I claim this to be the best possible, but it is something that worked for me, making the UVHM easy to solo.
NOTE: This guide does not include any Legendary or E-tech weapons, mods or relics because getting them is based on very low drop rate and hours of farming on specific bosses. (e.g.: Conference Call requires you to farm The Warrior or Handsome Jack.) This guide also does not include any quest-specific items, since getting them requires you to complete those quests first. Telling you to use some equipment that you won't get until late into the game would be rather pointless - if you're already to the endgame, why would you be needing this?
Quick analysis:
What's Zer0 great at, and where is he not so great?
Zer0 is really good at everything. Depending on your choice of skills and equipment, he can do just about anything fairly well - even tanking. This guide is geared towards a solo game though, so there won't be a lot of coverage on such co-op strategies.
His primary strength is dealing damage, in one of two ways: Either massively painful single blows every 15-20 seconds, or a constant stream of high DPS through damage bonus modifiers. Both styles work out to about the same rate of damage in the end, so which way you play is really up to you.
Weapons:
Forget any non-elemental guns. While you may love Jakobs guns for their ridiculously high raw damage stats, they're really not so useful in UVHM. UVHM puts heavy weight on exploiting your enemy's elemental weaknesses (and, conversely, greatly beefs up the enemies' elemental resistances) and effective use of multiple weapons. Slag damage is also greatly boosted. This is why you should notice that your weapon swap speed is slightly increased in UVHM. If you're playing UVHM, you're sure to find a whole new appreciation for Maliwan!
Always keep at least one each of Slag, Fire, Corrosive, and Shock weaponry on hand.
Make sure your Slag weapon has a high chance to slag. The gun damage is trivial - it can even be a level 1 gun, so long as it has a very high Slag percentage. You're not using the gun to deal the bulk of your damage in the fight. You're using it to enhance the damage your other guns deal. You don't want to throw yourself into the fray with a gun that constantly fails to apply Slag.
Pro Tip: Have 2 Slag weapons - one for close range, one for long range.
For your Shock weapon, you can use a Sniper Rifle. Shock damage has no penalty on flesh or armor, but deals massive damage on Shields. This means that a high-powered Shock Sniper Rifle can take out enemy Shields even without Slag. Still, you may want to carry a rapid-firing Shock SMG just in case. (Even though most heavy troopers don't carry shields - I guess it's an ego thing.)
For Fire weapons, I really recommend an SMG. After you've applied Slag, you can take down even Badass-level enemies with a rapid-firing Fire SMG. Moxxi's Good touch is great for this. You can get the Good Touch during any part of the game as long as you have access to Sanctuary. Just go to Moxxi's bar and tip her enough money (somewhere between $20k-$75k - anecdotal evidence varies). Good Touch always scales to your level, is extremely powerful, and returns 2% of the damage dealt back to you as a health recharge! You can go back to Moxxi any time to tip her again for a new one, which again will be scaled to your current level, so don't worry about "out-growing" this gun.
For corrosive weapons: SMG, SMG, SMG! Alternately, Shotgun. Most of the armored enemies you'll encounter are fast-moving Psychos (though now we call them Lunatics) or Hyperion loaders. Most of these will have hard-to-hit Critical locations, and will either be in your face with Melee or swarming you with Machine Gun fire and Grenades. This is not a good place to be relying on a Sniper Rifle. Instead, Slag the Lunatics and unload that SMG or Shotgun in their face - like everyone is Face McShooty! Loaders are about the same - they can quickly close the gap. Those pesky Surveyors aren't going to just hang around waiting for you to Snipe their armored core. Instead, blast them to bits with a Shotgun while they try their flyby attacks.
Grenades:
Yes! Lots of Grenades! Your best choice here is for Singularity or MIRV with a huge radius. Activate Decepti0n and drop grenades everywhere (this does not break Decepti0n) while you run for cover! This is extremely useful when getting pestered by those Stalkers, especially since you can see them while in Decepti0n even when they're invisible.
Pro Tip (especially for Solo players only): Throw a Slag Singularity, pause the game, switch to an Explosive MIRV and throw it where you dropped the Singularity. Watch the meat fountain! Instant profit!
Shields:
Anshin adaptive Shields. Not only do they give you a nice damage resistance bonus (matching resistance to the last damage type received), they also increase your health. Zer0 is all about health, especially considering that he is the only class with no passive Shield bonuses but all kinds of ways to regenerate huge amounts of health in seconds! If you're lucky enough to find a Purple-grade Anshin Shield (which offers up to 60% damage resistance) you can pretty much just stand idle while a Bruiser shotguns you to the face!
If you're more of a slash-and-dash player, you might prefer to use a shield that adds Roid damage. However, these usually have very short recharge delays which make them fairly difficult to use effectively (since the shield has to stay discharged to give you the bonus). The best use for Melee with Zer0 is to deliver the Killing Bl0ws to quickly dispatch enemies with low health. You don't need Roid shields for that, and you can even get a bonus with Resurgence which recovers health on every Melee kill.
Pro Tip: Carry one "elemental immunity" Shield of each element type on your backpack, regardless the level or type of Shields. You never know when you'll bump into a pack of enemies that are using just one elemental type. You'll really want that Shock immunity when the Super Badass Shock Skag decides to fry your brains with electric barks, while his Shock-charged Pups gnaw on your legs!
Relics:
Health relics - buff that HP! If you're using Anshin Shields as recommended, your Shield capacity is going to be low. Compensate for that by getting your Health as high as you can!
Class Mods:
Use a Survivor Class Mod. They all give extra HP and HP regeneration, and many come with some nice skill bonuses. Regenerating 600 HP/s may seem a bit slow when you have over 300k HP, but you'll be really glad your HP is constantly recharging when you're ducking for cover under heavy Buzzard fire. It's also real nice to know that, when you're traveling about, you won't have to shell out at the nearest Zed's when you get to town - by the time you get there, your health will already be full again!
The 8k HP bonus might not look like much, when you consider your enemies are blowing away 50k at a time. But when you survive that crazy blaster master rocket bombardment with just a few hundred HP left - giving you a chance to pop Decepti0n and run for cover, while regaining health - you'll be really glad you chose a Survivor mod!
Other decent Class Mod choices are Infiltrator and Ninja, if they suit your play style and Skill setups better.
Skills:
A full build layout is too much to cover in this post, but I'll give a few pointers.
B0re, B0re, B0re, B0re, B0re! No matter what your play style, take this one skill! You'll learn to love it, once you get the hang of it's effective use. It may also give you a pleasant suprise in a fight against Bunker. ;)
Execute. Take it, take it, take it, take it, take it! Combined with Killing Bl0w, this one can win you a lot of losing battles.
Innervate. At level 5, this skill lets you recover up to 24% of your max HP (which should be fairly high, if you've followed the above recommendations) whenever you drop into Decepti0n. Who can really say no to a fresh 24% HP refill available every 15 seconds? And if you've followed my recommendations so far, 24% of your max HP should be a lot of HP!
Rising Sh0t. Using those elemental SMGs like I told you to? Then meet your new best friend! At level 5, Rising Sh0t makes your 5th consecutive hit (and every consecutive hit afterwards) have a 50% damage bonus. With a really nice Survivor mod, this can be boosted to 110%! You want that extra damage! Unload your SMG on those baddies! With a 30-bullet mag, 25 bullets could be doing double damage or better! It's like having a co-op partner, or your own special way of Gunzerking! Multiply the damage with Slag and proper elemental selection, and the bad guys just don't stand a chance!
Unf0rseen - forget it!
Level 5 deals about 300k Shock damage, level 10 via Class Mods can deal almost 1M. But this has a very short radius, so usually the enemies you'll use this against are Suicide Psychos (which are going to, well, suicide anyway) or other relatively trivial grunts that just like being up in your face. 300k to 1M damage every 15-20 seconds is a pittance against Bosses and Badasses. With Slag, followed by the right elemental weapon, and Rising Sh0t, you'll be dealing that 300k on every shot instead!
Personal Note: I've played the game through up to level 61 with three different Zer0s. I've soloed Raid Bosses like Terramorphous, Pete, Hyperious, and Master Gee even without Legendary equipment! (Though once I did obtain some "Dahlicious" Orange goodness, they became even less of a hassle to defeat! Those Legendaries make a huge difference in terms of power - but that's another story.)
Best Answer
At the BL2 menu, just select New Game to start over with a new character.
Or if you want to keep playing your original character in order to finish any missions you missed, do a Save-Quit to get back to the main menu, then press a button (Y on the Xbox 360) to bring up a list of characters you have played, even if it's just the current character. When you select the current character from the list, your next option is to play the starting level or True Vault Hunter.